Solve for $x$ and $y$ using elimination. ${2x+3y = 23}$ ${3x-y = -4}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${2x+3y = 23}$ $9x-3y = -12$ Add the top and bottom equations together. $11x = 11$ $\dfrac{11x}{{11}} = \dfrac{11}{{11}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {2x+3y = 23}\thinspace$ to find $y$ ${2}{(1)}{ + 3y = 23}$ $2+3y = 23$ $2{-2} + 3y = 23{-2}$ $3y = 21$ $\dfrac{3y}{{3}} = \dfrac{21}{{3}}$ ${y = 7}$ You can also plug ${x = 1}$ into $\thinspace {3x-y = -4}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ - y = -4}$ ${y = 7}$